Desai and Lieber 



1 ^ 



2 d9 



Re 



3r2 



Bv, 

 Br 



4 sin 

 Re 



(1.71a) 



+ 4 sin (9 cos 6* 



1 !^ 



2 3t? 



Re \ Br2 



(1.71b) 



J. ^ 

 2 d0 



^3 



Re \ Br2 



Bv, 



(1.71c) 



The first terms on the left-hand sides of Eqs. (1.70a) and (1.71a) are the 

 contributions of the linear convective terms in Uj and Vj. The first terms on 

 the left-hand sides of Eqs. (1.70b) and (1.71b) are the contributions of the non- 

 linear convective terms in Uj and Vj to the pressure pj of the second itera- 

 tions. Similarly, the terms on the left-hand sides of Eqs. (1.70c) and (1.71c) are 



the contributions of the linear convective terms in u, and 



and the nonlinear 



convective terms in u^ and v,. These terms are zero. It is clear by compari- 

 son that the order of magnitude of the linear and nonlinear convective terms in 

 Uj and Vj is the same. Because of this, the second iteration must make about 

 the same order of magnitude contribution to the pressure field p as the first 

 iteration, but of opposite sign, as Eqs. (1.70a), (1.70b), (1.71a), and (1.71b) indi- 

 cate. Since there is no contribution to pressure from convective terms in Eqs. 

 (1.70c) and (1.71c), the pressure field p^ may be assumed to contribute very 

 little to the total pressure p if we bear in mind that the boundary conditions re- 

 quire U3 and V3 to vanish at the wall as well as far away from the cylinder. 

 Higher iteration pressure fields p^, will behave essentially as P3, but with de- 

 creasing intensity. This discussion is based on the pressure around the cylin- 

 der and is not regarded here as rigorous. However, it is strongly indicative of 

 the importance of the second iteration and the relative unimportance of the 

 higher iterations. We may say that two iterations are sufficient in this case to 

 give results close to the actual solution. 



The case we have just discussed relates to the stream function 0' as given 

 by Eq. (1.45). This is, in fact, the potential flowstream function. Along similar 

 lines we will now consider 41^, u^, and Vq to be given by 4j' , u', and v' as in 

 Eqs. (1.46). We then have at r = 1 



u,| - u'l =+2cos6' 



(1.72) 



Applying Eqs. (1.72) to Eqs. (1.63), (1.64), and (1.65), we find that in Eqs. 

 (1.67a) instead of Bj(l,t) = +2 and Bj(l,t) = we should have Bi(i,t) = 

 and Bj(i,t) ~ 2. These conditions imply that for this case 



548 



